Related papers: Link Algebra: A new aproach to graph theory
Knowledge graphs have been shown to play a significant role in current knowledge mining fields, including life sciences, bioinformatics, computational social sciences, and social network analysis. The problem of link prediction bears many…
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
We present a mathematical framework for mapping second-order logic relations onto a simple state vector algebra. Using this algebra, basic theorems of set theory can be proven in an algorithmic way, hence by an expert system. We illustrate…
A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…
Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
Link prediction, the problem of identifying missing links among a set of inter-related data entities, is a popular field of research due to its application to graph-like domains. Producing consistent evaluations of the performance of the…
The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic…
We establish connectedness criteria for graphs associated to monomials in certain quotients of the mod 2 dual Steenrod algebra. We also investigate questions about trees and Hamilton cycles in the context of these graphs. Finally, we…
We propose a novel structure, the data-sharing graph, for characterizing sharing patterns in large-scale data distribution systems. We analyze this structure in two such systems and uncover small-world patterns for data-sharing…
We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…
A $k$-connected set in an infinite graph, where $k > 0$ is an integer, is a set of vertices such that any two of its subsets of the same size $\ell \leq k$ can be connected by $\ell$ disjoint paths in the whole graph. We characterise the…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or not such spaces are connected.
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
Arithmetical structures on a graph were introduced by Lorenzini as some intersection matrices that arise in the study of degenerating curves in algebraic geometry. In this article we study these arithmetical structures, in particular we are…
The notion of associativity (which differs from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for operations of high arity is introduced. It is proved that the…
Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing…